Alignment: Overall Summary

The instructional materials reviewed for Grade 8 partially meet the expectations for alignment to the CCSSM. While the instructional materials met the expectations for focus and coherence, they did not meet the expectations for rigor and the mathematical practices.

The instructional materials reviewed for Grade 8 had approximately 70% of the work on the major clusters for 8.EE.A, 8.EE.B, 8.EE.C, 8.F.A, 8.F.B, 8.G.A and 8.G.B. The content could be covered in 145 days. There are two chapters that connect two or more domains within Grade 8. In the teacher edition, the CCSSM are listed for each lesson. In the student edition, the lesson objective is listed each time and these objectives are based on the CCSSM.

The materials reviewed for Grade 8 do not meet expectations for rigor, balance and practice-content connections. Each lesson is launched with a real-world situation but they are often application problems and do not also build conceptual understanding. The materials have very few conceptual problems. There are inconsistencies among chapters and concepts on how much conceptual understanding is presented. Procedural skills are evident throughout the chapters; however, most if not all of the problems are skills-based without attending to conceptual understanding. Non-contrived and/or non-routine real-world application problems were not present in all chapters. There is no evidence of students making their own assumptions or simplifying to model mathematically in the chapters. The program is not balanced between conceptual understanding, procedural skill and fluency and application. The MPs for each chapter are listed in the chapter at a glance pages. The MPs are there as a structure to design procedural problem work. The lessons do not allow students to construct meaning from the MP. During lessons, there is no specific mention of the MPs and it is not clearly evident how students might use the practices. Many of the lessons and homework are procedural in nature and do not offer many opportunities for students to apply the practices in order to extend learning and understanding. There are few instances where students have to justify an explanation and even fewer where they critique others. Mathematical vocabulary is used appropriately at the Grade 8 level. This text excels in mathematical language - it is used consistently throughout instruction, examples, practice and assessment.

The Report

Gateway One

Focus & Coherence

Meets Expectations

The materials reviewed for Grade 8 meet the expectations for focusing on major work and coherence. The instructional materials reviewed for Grade 8 had approximately 70% of the work on the major clusters for 8.EE.A, 8.EE.B, 8.EE.C, 8.F.A, 8.F.B, 8.G.A and 8.G.B. The content could be covered in 145 days. There are two chapters that connect two or more domains within Grade 8. In the teacher edition the CCSSM are listed for each lesson. In the student edition the lesson objective is listed each time and these objectives are based on the CCSSM.

Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.

The instructional materials reviewed for Grade 8 meet the expectations for assessing material at the Grade 8 level. The items tested are aligned to the CCSSM for Grade 8.

Indicator 1a

The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.

Criterion 1b

The instructional materials reviewed for Grade 8 meet the expectations for spending the majority of class time on the major clusters for Grade 8. The instructional materials reviewed for Grade 8 spend approximately 70% of the time on the major clusters for 8.EE.A, 8.EE.B, 8.EE.C, 8.F.A, 8.F.B, 8.G.A and 8.G.B.

Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.

Criterion 1c - 1f

The materials reviewed for Grade 8 partially meet the expectations for coherence. The content could be covered in 145 days. “Concepts and Skills Across the Curriculum” link the current material to the skills progression to both the previous and the next grade. In the teacher edition, the CCSSM are listed for each lesson. In the student edition the lesson objective is listed each time and these objectives are based on the CCSSM.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The instructional materials reviewed for Grade 8 partially meet the expectations for the supporting content enhancing the major work.

The first nine chapters are on major work.

In chapters 10 and 11, students create scatter plots and are asked to put in a line of best fit and write an equation for this line. Supporting content 8.SP.A makes connections to the major work of 8.F.B where students are using scatter plots to interpret relationships within a function. It also connects to 8.EE.B when it has students write equations for a line of best fit on the scatter plots.

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.

The materials reviewed for Grade 8 meet the expectations for the amount of content designated being viable for one school year.

The content could be covered in 145 days.

This meets the threshold for more than 65% of the year being focused on the major work of 8th grade to foster coherence between Grade 8 and Grade 9.

Indicator 1e

Materials are consistent with the progressions in the Standards
i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work
ii. Materials give all students extensive work with grade-level problems
iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.

The materials reviewed for Grade 8 meet the expectations for the progressions in the standards.

"Concepts and Skills Across the Curriculum" links the current material to the skills progression to both the previous and the next grade.

Chapter 11 on probability is identified as meeting Grade 7 standards.

Every chapter starts with a section of recalling prior knowledge for the students with a review and a quick check practice.

Math background pages give teachers a review of the background knowledge needed for the unit.

Indicator 1f

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards
i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings.
ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.

Gateway Two

Rigor & Mathematical Practices

Does Not Meet Expectations

The materials reviewed for Grade 8 do not meet expectations for rigor, balance and practice-content connections. Each lesson is launched with a real-world situations but they are often application problems and do not also build conceptual understanding. The materials have very few conceptual problems. There are inconsistencies among chapters and concepts on how much conceptual understanding is presented. Procedural skills are evident throughout the chapters; however, most if not all of the problems are skill based without attending to conceptual understanding. Non-contrived and/or non-routine real world application problems were not present in all chapters. There is no evidence of students making their own assumptions or simplifying to model mathematically in the chapters. The program is not balanced between conceptual understanding, procedural skill and fluency and application. The MPs for each chapter are listed in the chapter at a glance pages. The MPs are there as a structure to design procedural problem work. The lessons do not allow students to construct meaning from the mathematical practice. During lessons, there is no specific mention of the MPs and it is not clearly evident how students might use the practices. Many of the lessons and homework are procedural in nature and do not offer many opportunities for students to apply the practices in order to extend learning and understanding. There are few instances where students have to justify an explanation and even fewer where they critique others. Mathematical vocabulary is used appropriately at the Grade 8 level. This text excels in mathematical language - it is used consistently throughout instruction, examples, practice, and assessment.

Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.

The materials reviewed for Grade 8 do not meet expectations for rigor and balance. Each lesson is launched with a real-world situation but they are often application versus building conceptual understanding. The materials have very few conceptual problems. There are inconsistencies among chapters and concepts on how much conceptual understanding is presented. Procedural skills are evident throughout the chapters however, most if not all of the problems are skill based only with no conceptual understanding. Non-contrived and/or non-routine real world application problems were not present in all chapters. There is no evidence of students making their own assumptions or simplifying to model mathematically in the chapters. The program is not balanced between conceptual understanding, procedural skill and fluency and application.

Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

Each lesson is launched with a real-world situation, and these often support application practice and do not build conceptual understanding.

Problems are solved for students, and they are shown each step in prescribed process. The materials have few conceptual problems.

There are strategies provided for teachers to help students understand concepts better, but few problems for students to explore on their own.

Lessons include practice with procedural work and homework assignments include application.

There are inconsistencies among chapters and concepts on how much conceptual understanding is presented.

Lesson 5.1 introduces solving systems of equations through tables to build conceptual understanding, but the rest of the chapter focuses on procedures.

Lesson 4.4 on understanding slope-intercept form begins with a problem situation about two boys walking at a constant rate but this problem only describes vocabulary of y intercept, x intercept and slope intercept form. The students are not asked to solve a problem using this vocabulary except in rote problems.

There are a variety of representations used.

Practice problems are intermingled with contextual problems, tables and number work with scaffolding. Many questions ask for the answer without having students explain or justify.

Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

The materials reviewed for Grade 8 partially meet the expectations for giving attention to individual standards for developing procedural skills and fluency.

Procedural skills are evident throughout the chapters; however, most problems are skills-based without attending to conceptual understanding.

There are instances where students are engaged in problems that require procedural skills and fluency.

Most of the problems in the lessons and over half of the homework is typically devoted to procedural skills and fluency.

Fluency is built from practicing the procedures shown to the students in the examples of the lessons.

Lesson 8.3 builds a conceptual understanding of rotation and then works on procedural fluency of rotating shapes.

In chapter 9 students are asked to justify their ideas about transformations as they are working on doing the transformations.

Each chapter has a lot of repeated practice for building procedural fluency.

Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade

The materials reviewed for Grade 8 do not meet the expectations for students spending sufficient time working with engaging applications of the mathematics.

Non-contrived and/or non-routine real-world application problems were not evident in all chapters.

There is no evidence of students making their own assumptions or simplification to model mathematically in the chapters.

Some chapters had more application problems than others.

There are "Brain Work" problems in each chapter. They are problems that could be multi-step and non-routine but they are scaffolded with step-by-step questions that do not support students in solving the problems themselves.

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.

Criterion 2e - 2g.iii

The materials reviewed for Grade 8 do not meet the expectations for practice-content connections. The MPs for each chapter are listed in the chapter at a glance page. The MPs are there as a structure to design procedural problem work. The lessons do not allow students to construct meaning from the MP. During lessons, there is no specific mention of the MPs and it is not clearly evident how students might use the practices. Many of the lessons and homework are procedural in nature and do not offer many opportunities for students to apply the practices in order to extend learning and understanding. There are few instances where students have to justify an explanation and even fewer where they critique others. Mathematical vocabulary is used appropriately at the Grade 8 level. This text excels in mathematical language - it is used consistently throughout instruction, examples, practice, and assessment.

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.

The materials reviewed for Grade 8 partially meet the expectations for having the Standards for Mathematical Practice (MPs) identified and used to enrich mathematics content.

The MPs for each chapter are listed on the chapter at a glance page.

The MPs are there as a structure to design procedural problem work.

The lessons do not allow students to construct meaning from the MP.

During lessons, there is no specific mention of the MPs and it is not clearly evident how students might use the practices.

The lessons do not always match the practices that are listed. For example, chapter 2 says MP1 is spotlighted. The problems are small, scaffolded and the application of a procedure. The students are not applying problem solving strategies or having to persevere through long problems.

Instances that support MPs include lesson 9.2: Construct arguments, where students have to identify similar triangles and justify how they can prove it; Lesson 5.2: Model mathematics, which sets up systems using bar models; and Lesson 6.2: Model mathematics, which addresses multiple representations of a function, such as words, equations, tables and graphs.

Indicator 2f

Materials carefully attend to the full meaning of each practice standard

The materials reviewed for Grade 8 do not meet the expectations for carefully attending to the full meaning of each practice standard.

The MPs are listed at the beginning of each chapter on the chapter at a glance page.

MPs are not referenced throughout lessons, homework, or assessments.

Many of the lessons and homework are procedural in nature and do not offer many opportunities for students to apply the practices in order to extend learning and understanding.

In the majority of lessons, the work is teacher and text driven, and the students are provided step-by-step processes and just expected to mirror what is provided to them.

An example is in lesson 4.3. The teacher edition states that the students are using MP1. The lesson is on writing equations of a line in slope-intercept form. The lesson does not have them persevere through a problem instead they fill in blanks to follow a set way to create the equations.

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:

0/0

Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

The materials reviewed for Grade 8 partially meet the expectations for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others.

The materials are scaffolded to the point where true, rich discussion may not be possible.

For example, in lesson 5.3, the teacher edition states, "Best Practices--You may want to ask volunteers to show how this system of equations could be solved using the substitution method." This statement implies that this strategy may or may not be employed. It in no way encourages teachers to use this authentic discussion daily.

In most lessons, there are hints to the teacher that would prompt some analysis to begin discussions such as in lesson 6.2; teachers have a prompt telling them to have a student explain in their own words the "Caution" in the example problem.

Many of the "Best Practices" boxes provide suggestions to teachers that ask the students to think about what is presented.

In Lesson 4.4, it prompts teachers to have students verify the slope by using two points or in Lesson 5.2, the prompt is to solve it in another way.

Some of the "Think Math" strategies could help students construct viable arguments but there is no guarantee that these strategies will be utilized by teachers.

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.

Gateway Three

Usability

Not Rated

This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.

N/A

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.

N/A

Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.

N/A

Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

N/A

Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

N/A

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.

N/A

Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.

N/A

Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.

N/A

Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.

N/A

Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).

N/A

Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

N/A

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

Criterion 3m - 3q

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.

N/A

Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.

N/A

Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

N/A

Indicator 3p

Materials offer ongoing formative and summative assessments:

N/A

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.

N/A

Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

N/A

Indicator 3q

Materials encourage students to monitor their own progress.

N/A

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

N/A

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.

N/A

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

N/A

Indicator 3u

Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).

N/A

Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.

N/A

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.

N/A

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.

N/A

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.

N/A

Criterion 3z - 3ad

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.

Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

N/A

Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.

N/A

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

N/A

Indicator 3ac

Materials can be easily customized for individual learners.
i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.
ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.

N/A

Indicator 3ad

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).

Additional Publication Details

Report Published Date:
02/15/2015

Report Edition: 2013

Title

ISBN

Edition

Publisher

Year

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9780547618104

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9780547618142

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About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

Rubric Design

The EdReports.org’s rubric supports a sequential review process through three gateways. These gateways reflect the importance of standards alignment to the fundamental design elements of the materials and considers other attributes of high-quality curriculum as recommended by educators.

Advancing Through Gateways

Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?

Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Key Terms Used throughout Review Rubric and Reports

Indicator Specific item that reviewers look for in materials.

Criterion Combination of all of the individual indicators for a single focus area.

Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.

Alignment Rating Degree to which materials meet expectations for alignment, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

Focus and Coherence

Rigor and Mathematical Practices

Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.